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Minimum reinforcement and ductility index of lightly reinforced concrete beams

  • Fantilli, Alessandro P. (Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino) ;
  • Chiaia, Bernardino (Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino) ;
  • Gorino, Andrea (Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino)
  • Received : 2016.07.13
  • Accepted : 2016.09.11
  • Published : 2016.12.25

Abstract

Nonlinear models, capable of taking into account all the phenomena involved in the cracking and in the failure of lightly reinforced concrete beams, are nowadays available for a rigorous calculation of the minimum reinforcement. To simplify the current approaches, a new procedure is proposed in this paper. Specifically, the ductility index, which is lower than zero for under-reinforced concrete beams in bending, is introduced. The results of a general model, as well as the data measured in several tests, reveal the existence of two linear relationships between ductility index, crack width, and the amount of steel reinforcement. The above relationships can be applied to a wide range of lightly reinforced concrete beams, regardless of the geometrical dimensions and of the mechanical properties of materials. Accordingly, if only a few tests are combined with this linear relationships, a new design-by-testing procedure can be used to calculate the minimum reinforcement, which guarantees both the control of cracking in service and the ductility at failure.

Keywords

References

  1. ACI (2014), ACI 318-14: Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Farmington Hills, Michigan, USA.
  2. Bazant, Z.P. and Cedolin, L. (1991), Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, Oxford University Press, New York, U.S.A.
  3. Beeby, A.W. (2004), "The influence of the parameter $\phi$/${\rho}_{eff}$ on crack widths", Struct. Concrete., 5(2), 71-83. https://doi.org/10.1680/stco.2004.5.2.71
  4. Beeby, A.W. (2005), "Discussion-the influence of the parameter $\phi$/${\rho}_{eff}$ on crack widths", Struct. Concrete, 6(4), 155-165. https://doi.org/10.1680/stco.2005.6.4.155
  5. Borosnyoi, A. and Balazs, G.L. (2005), "Models for flexural cracking in concrete: the state of the art", Struct. Concrete, 6(2), 53-62. https://doi.org/10.1680/stco.2005.6.2.53
  6. Bosco, C., Carpinteri, A. and Debernardi, P.G. (1990), "Minimum reinforcement in high-strength concrete", J. Struct. Eng., 116(2), 427-437. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:2(427)
  7. Brincker, R., Henriksen, M.S., Christensen, F.A. and Heshe, G. (1999), "Size effects on the bending behaviour of reinforced concrete beams", Eur. Struct. Integr. Soc., 24, 127-180.
  8. Carpinteri, A. (1989), "Minimum reinforcement in reinforced concrete beams", RILEM TC 90-FMA, Code Work, Cardiff, September.
  9. Carpinteri, A. (1999), Minimum Reinforcement in Concrete Members, Elsevier, Oxford, U.K.
  10. Carpinteri, A., Cadamuro, E. and Corrado, M. (2014), "Minimum flexural reinforcement in rectangular and T-section concrete beams", Struct. Concrete, 15(3), 361-372. https://doi.org/10.1002/suco.201300056
  11. Carpinteri, A., Ferro, G., Bosco, C. and Elkatieb, M. (1999), "Scale effects and transitional failure phenomena of reinforced concrete beams in flexure", Eur. Struct. Integr. Soc., 24, 1-30.
  12. CEB (1998), CEB Bulletin 242: Ductility of Reinforced Concrete Structures, European Committee for Concrete, Lausanne, Switzerland.
  13. CEN. (2004), EN 1992-1-1: Eurocode 2: Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings, European Committee for Standardization, Brussels, Belgium.
  14. Elrakib, T.M. (2013), "Performance evaluation of HSC beams with low flexural reinforcement", HBRC J., 9(1), 49-59. https://doi.org/10.1016/j.hbrcj.2012.12.006
  15. Fantilli, A.P. and Chiaia, B. (2013), "Golden ratio in the crack pattern of reinforced concrete structures", J. Eng. Mech., 139(9), 1178-1184. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000548
  16. Fantilli, A.P., Cavallo, A.D. and Pistone, G. (2015), "Fiber-reinforced lightweight concrete slabs for the maintenance of the Soleri Viaduct", Eng. Struct., 99, 184-191. https://doi.org/10.1016/j.engstruct.2015.04.045
  17. Fantilli, A.P., Ferretti, D. and Rosati, G. (2005), "Effect of bar diameter on the behavior of lightly reinforced concrete beams", ASCE J. Mater. Civ. Eng., 17(1), 10-18. https://doi.org/10.1061/(ASCE)0899-1561(2005)17:1(10)
  18. Fantilli, A.P., Ferretti, D., Iori, I. and Vallini, P. (1999), "Behaviour of R/C elements in bending and tension: The problem of minimum reinforcement ratio", Eur. Struct. Integr. Soc., 24, 99-125.
  19. Fib (2000), Fib Bulletin 10: Bond of Reinforcement in Concrete, International Federation for Structural Concrete, Lausanne, Switzerland.
  20. Fib (2012), Fib Bulletin 65-66: Model Code 2010-Final Draft, International Federation for Structural Concrete, Lausanne, Switzerland.
  21. Giuriani, E. and Plizzari, G.A. (1998), "Interrelation of splitting and flexural cracks in RC beams", J. Struct. Eng., 124(9), 1032-1040. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:9(1032)
  22. Lange-Kornbak, D. and Karihaloo, B.L. (1999), "Fracture mechanical prediction of transitional failure and strength of singly-reinforced beams", Eur. Struct. Integr. Soc., 24, 31-66.
  23. Levi, F. (1985), "On minimum reinforcement in concrete structures", J. Struct. Eng., 111(12), 2791-2796. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:12(2791)
  24. Maldague, J.C. (1965), "Etablissement des lois moments-courbures", Annales de l'Institut Technique du Batiment et des Travaux Publics", 213, 1170-1218.
  25. Rizk, E. and Marzouk, H. (2011), "Experimental validation of minimum flexural reinforcement for thick HSC plates", ACI Struct. J., 108(3), 332-340.
  26. Ruiz, G., Elices, M. and Planas, J. (1999), "Size effect and bond-slip dependence of lightly reinforced concrete beams", Eur. Struct. Integr. Soc., 24, 67-97.
  27. Said, M. and Elrakib, T.M. (2013), "Experimental verification of the minimum flexural reinforcement formulas for HSC beams", IJCIET, 4(5), 152-167.
  28. Seguirant, S.J., Brice, R. and Khaleghi, B. (2010), "Making sense of minimum flexural reinforcement requirements for reinforced concrete members", PCI J., 55(3), 64-85. https://doi.org/10.15554/pcij.06012010.64.85
  29. Yasir Alam, S., Lenormand, T., Loukili, A. and Regoin, J.P. (2010), "Measuring crack width and spacing in reinforced concrete members", Proceedings of the 7th International conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-7), 377-382.